{
 "metadata": {
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.4-final"
  },
  "orig_nbformat": 2,
  "kernelspec": {
   "name": "python_defaultSpec_1600519684882",
   "display_name": "Python 3.7.4 64-bit ('base': conda)"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 2,
 "cells": [
  {
   "source": [
    "# 多项式回归"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "x = np.random.uniform(-3, 3, size=100)\n",
    "X = x.reshape(-1,1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "y = 0.5 * x**2 + x + 2 + np.random.normal(0 ,1, size =100)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "LinearRegression(copy_X=True, fit_intercept=True, n_jobs=None, normalize=False)"
     },
     "metadata": {},
     "execution_count": 6
    }
   ],
   "source": [
    "from sklearn.linear_model import LinearRegression\n",
    "\n",
    "lin_reg = LinearRegression()\n",
    "lin_reg.fit(X, y)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "y_predict = lin_reg.predict(X)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(X, y)\n",
    "plt.plot(x, y_predict, color='r')\n",
    "plt.show()"
   ]
  },
  {
   "source": [
    "## 添加一个特征"
   ],
   "cell_type": "markdown",
   "metadata": {}
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(100, 1)"
     },
     "metadata": {},
     "execution_count": 10
    }
   ],
   "source": [
    "(X**2).shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "X2 = np.hstack([X, X**2])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "(100, 2)"
     },
     "metadata": {},
     "execution_count": 12
    }
   ],
   "source": [
    "X2.shape"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "lin_reg2 = LinearRegression()\n",
    "lin_reg2.fit(X2, y)\n",
    "y_predict2 = lin_reg2.predict(X2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "output_type": "display_data",
     "data": {
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c9HMnoEyhAC6SpdJRHx3yOfdoBKecAosXe5sxnHJKVOeKdVlav5bDzSRKoYhkIb82Z0j0Of/8t3f44ahjYckSeOONqIM3xL42Sy5WpKgHLpKFUt0bLZ1dXq/ipMPqcv4xaiCucgP8621vL8sYxbI2Sy5WpKgHLpKFou2N+rEHZnXPu2bw7rzyC8b881aabP6JPn0eiCt4xyoXK1LUAxfJQtH0Rv0a9Kvb2+9S/gnPjxnEhvwmXHLxYDbus3+8lxGTRHcCykQK4CJZKJoBwETSLDUHK2tO0zl+8SyeLn2AlTu15JI+9/Fdq7YMTmEPONf2xVQAF8lC0fRG4x30q9tzr3bmgn/zyGt/ZFGrvbjsgntY06wlf8yBneHTSQFcJEs11BuNd9AvVM/90g9e4+7Jz1C25wFc1etOKpvvouCdAhrEFMlR8Q761eqhO8fN/x7BvZOf5p19j+SyC+6l+R6tU74VW65SD1wkR8U76Ffdc8+r2sJ9b/6FCz98i5cOOYUnet/CJ384NaY25PJmDH5QABfJYfEM+vXv3ol7R81gyMtDOHXRDB4/pjdPntSXwWccGNN5cnHqu9+UQhGRmJTsbrwzYRAnfV7GHaf+hlFnX8PgXofGHHSjWW1QIlMPXESi9+GHcOaZFK5dC6+9yr1nnMG9cZ4qF6e++009cBGJzqRJcNxx4Bz8+9/eXpYJCFftks1T3/2mAC4iDXvmGejRA/beG6ZNg8MPT/iUuTj13W9KoYikWEZVXlRVwa23wsMPez3uUaOgeXNfTp2LU9/9pgAukkIZVXmxYQNcdpm39dlvfwuPPgqN/Q0ZuTb13W9KoYikUMZUXqxYASeeCOPHwyOPwOOP+x68JXF6RURSKCMqLz76yMt3r1jhBfCSkrCHBjEdFMQ2JYt64CIpFPjKi1de8dbu3rgR3nuvweCd6l1/GhLENiWTArhICgW28sI5uO8+L2B37gwzZ0JxccSHBDEdFMQ2JZNSKCIpFMjKix9/hCuugDFj4OKL4dlnoaDhTwRBTAcFsU3JlHAAN7M8oAwod871SLxJItktUJUXixZBr14wfz4MHQr9+oFZVA8N4h6UQWxTMvmRQrkRWODDeUQklV57zUuTLF0Kr78Ov/991MEbgpkOCmKbkimhAG5mewJnAs/50xwRSbotW2DQIDjrLG9m5axZ0L17zKcp6VLE4J6HUFRYgAFFhQVpXwc8iG1KJnPONXxUuAebjQUGA82B34dKoZjZNcA1AO3atfvZkiVL4n4+EUnQ6tVennvSJLj8cnjyyajy3ZJeZjbLOVdvVDnuHriZ9QBWOudmRTrOOTfMOVfsnCtu3bp1vE8n4pvS2eV0GzKFjgMm0m3IlKwtMatpYOk8zr7iz3y194FseuttXvn1QBg+XME7wyWSQukGnG1mXwKjgJPM7EVfWiWSJLlWJwww8OUP4amnGfOPfjSu2kLvi4ZwY+HRDHxlfrqbJgmKO4A7525zzu3pnOsA9AGmOOcu8a1lIkmQa3XCrF/P0X/4Hfe99ST/a3cYZ17+GLOLOgMwcvrSNDdOEqU6cMkpOVUnPGMGXHQRpy/+goeOv4ynjj4PZ9v7bFsSGP+SYPBlJqZz7l3VgEsmCPxUdj9UVcGQIdCtG1RWcuFFg3nymAtqBW+ARtFXDEpAaSq95JRsqxOuOyA76a1ZcOqpcNttcO65MGcO8zoeEvKxOzbW2z/TKYUiOSWQU9njVHdt8QNmvstR9zzGZldJ4+eeg1/9CszYWFkV8vHhbpfMoQCeoFxaujJbBGoqewKqB2R3rPyJ298dTt8PJjJ/9324/+I7GHll323H5dr08lyiz1AJyMWSNAmO5WsrOPibRbz695vp+8FEnj2yhJ6XPMy0/Fa1jsu2tJFsl9U98GT3jiOVpGVDD08CrLKSP5SNoe+/XuS7prtw2fl3897ePwO86eM1ZVPaSGrL2gCeir0Hc6okLU5KMSXBxx/DZZdx1axZTDj4RAae/GvWNWkGhO9ZZ0vaSGrL2hRKKiZs5ERJWgKUYvLZ5s3ekq9HHAFLlsDYsVS98A+a79E6JxZukvqytgeeit5x/+6davXyQbnFmpRi8tH8+V5VycyZ3q45Tz8Nu+9OCQHczV5SJmsDeCpG3pVbjEwppuiFTTVt2gQPPgj33gu77AKjRsEFF8S0brdkr6wN4KnqHSu3GJ7K16ITbrym5dwyjh96u5fz7t0bHn8ctKKn1JC1OfBcW9g9iFS+Fp26qabmP/3I7RMf5/grSmD9enj1VRg1itJlm3JuGVyJLGN74NFUN6h3nF5BTTEFrTJmW0rJOc5e8B4DpzzHrhu+56/F53Dlv16EZs1SUlUlmScjAnjdN9yJnVszbla5fpkzQND+iAYxELYtLKDJ559y9+SnOW7JXObusR9X9rqT1QccypXNvPJADQhLKIFPoZTOLueu0WVcUvoULTZ8T/naCkZM+yq31nQW3wRuPfB163j+45eYNPx6Dv1mEQNP/Q3nXvowi9p1rpVq0oCwhBL4HvjQNxdyyBcfctXMl7l4zhs81u1CXjjiTCrz8usdm8pf5qB9DJfohBpUhTQEwqoqePFFuPVW9luxgi/P6c1vDzqPjzc3Cfn7pAFhCSXwAXz52grKOx7Bab96goFTnuOOKc9x0Zw3uP/EK5myz5G1yqlS9cscxI/h0rDS2eUYEGobg5QGwmnT4KabYPp06NoVJkygw5FHMjHCQzTnQEIJfAql+o31+a57ccX5d3P5eXcBxvBx9/DCS3ey/6ovgdq/zNFsWpvIxraB+xguURn65sKQwRvgxM4pKM+bM4evT/glHHMMK+d/yv3n9af0ybFw5JENPlRVVRJK4Hvg/bt3ov+YuVRWeW+9d/cpZvreXXj42/f5+T+fZNLw3zHpiFPJu+ceuncpiqp3nGgPuqF8pNIrwRQpTTJuVjnF7VvWe518eS3nz4dBg2D8eJo2acbQn1/K8z87ix93bEpB6UfQqFFU5wzagLCkX+ADOAB1Jp1tbtyYyutvYOeHboEhQzjj8ceh5/Fw3XUMa3Y8FZU71Dq+7mh9oiP6kfKR6UqvhKrU+dcnq/RHpIZwrxuEfv0Tfi0XLoS77oLRo6FZM4afdCmPHnLmtoWnwj2vSLQCn0IZ+uZCKrfU/uBbucV56Ypdd/UW9/nsM7jkEvjznxn90MX87v2RNN1U+41as/eV6Ih+pAkq6UivhFo06sVpX2kRqToaSpPUff3DvZY3vzQn8s/y88+hb1848EBvEs6AAfDll9x7ZO9awTvc84pEK/ABPKpgu9de8Ne/wrx5fLDvEfT7zwimDruay2a9yo6bNwG1B6kSXUUwUj4yHeVeoQJNXcrRw78+WRXx/rqvf7jXzDnoP3Zu/SC+ZAlcdRV06gQvvQQ33wyLF8MDD0DLllq9UnwX+AAe0y/9gQey5sXR9Ln8T3zeck/uefsZ3n3maq6c+zq3ntBu22F+TPEu6VLE+wNO4oshZ/L+gJO2fQROx5s02j8Oud7Ti3T9oV7/SK/Ztk+BAOXlcN11sN9+8I9/eP9fvBgefhh2223bY7S0gPgt8AE81l/6ki5F9LnhAvr95lEu7n0fK3dtwx2TnuTsc4+Dhx6CdeuSOqKfjjdptH8ccr2nF+7688xCvv4NvWabli33ygH32Qeeew6uvNJLn/z5z9CmTb3jVUkifjPnwhVW+a+4uNiVlZXF/LiEKgGcg/fe8z7GvvUWFBbC734HN9wArVo1/Pg4pLoKpe5gWygF+Xk5HyxC/Zwa+rl0uect1myorHVbyw3f8+vp4+g7eyJNqjZ7+e477oAOHZLZfMlhZjbLOVdc7/ZMCOC+KSuDwYNh/Hho2hR+/WsvkGfBG09VKNGJ9Y9r6ezybWWsLTZ8z5Vlr3BF2QSabN5E+Rnn0u7RIbDvvim8AslFCuA1ffyxt0j+iBHelOYzzoBrr4XTT4e8vIYfLznl7fFTWfPAQ/SY+w47bt7E5IOPJ+/uuzml5wnpbprkCAXwUJYuhWef9fKXX38N7dvDNdd4W1ftsUe6WyfpVFkJr7zibV32zjuw445eqer//Z9XHpgkkT4haIJY7lIAj6SyEiZMgKee8t6sjRtDz57wm9/ACSckffsqvTHTI+TPfdct2/+of/MNtGsHV1/t/WGvUVGSrPbUzdHn5xk77dCYtRWV9dZx0bhG7vA9gJvZXsALwB5AFTDMOfdYpMcENoDXtHAhPPMMPP88rFkDBxzgpVcuu8wbAPVZNANrCvD+q/lzb1S1heO/+IC+c9/gF5+XYc6lJa3WbciUsDNFwykqLOD9ASclqUUSFMkI4G2ANs65D8ysOTALKHHOfRzuMRkRwKtVVHhToJ96CmbMgIICuPBCr1deXO/nGLdwb9rqN2Y8lRPSsG5DprB56VJ6zZ/CRXMmsee6lazaqZDXjzyDvs8/4KXTUqzjgIlhF9uKpKiwQH/cs1zSUyhm9grwhHNucrhjMiqA1/TBB14udMQI2LDBC+BXXgnnn+9N509ApDdtUYS1O9TzitMPP0BpKe/d8Se6LZlLnqvi/faHMuLwM5i831FszsvniyFnpqVp8fTAlVbJDeECuC8TecysA9AFmO7H+QLniCNg2DBYvtzbGbyiwuuJt2kDZ5/tBfb16+M6dbjJJUb4zQdAsypjsno1vPAClJR4u7pfein7fv81fzn6fH5x9TNc3OcBXu98HJV5+Wmd7BRqElgkodY215IJuSXhAG5mzYBxwE3OuXUh7r/GzMrMrGzVqshrUQTeLrvA9dfDvHler/yGG7x/L7nEG+AqKfECxerVUZ8y1Js23KYDNeX6rMoGff21l/469VTYfXdvsk1ZmTcg+d57zJg8g6dOvpwvW27vqaZ7WnvdmZotmuaT36j2AHr1d0WFBWF/R/THPXcklEIxs3zgNeBN59yfGjo+Y1MokVRVwX//6y1e9PLLsGyZN+h14oleQD/rLK+SIYK6g5QNfYw24JHeh6d0edqMyK1+/rn3Gowf7+164xzsv79XUXTuuV7qq9H2PkvQr7F0djl3TfiItRXeTNAWTfMZdNZB29rY0PiJZI9kDGIa8HdgtXPupmgek5UBvCbnvF5edRBZuPWj7EEHedUMp50G3bpBkyYRTxNNLvTLJOZpM2Lg1DlvEakZM7ytySZNgg8/9O7r0sUL2j17elVESS4DTYZoq5MC/zqJL5IRwI8D/g3MwysjBLjdOfd6uMdkfQCva+FCeO01eOMNbz2WykqvmuW44+Ckk+Dkk71g07j2vhoNrW0SqoflZ28ykD27NWu8P44zZmz/+uYb7778fDjqKC9gl5RAx46+PnU6eurRvgZB/xQh/ggXwOPekcc59x/q7ZUjtXTq5H316+cNck6dCpMnw5QpcNtt3jHNmsGxx3pB/dhjobh42xvw7lc/qreQUqg8rd+7AKVjTfNaNm6EOXNqB+vPPtt+f6dOXm67a1dvP8nDDmvwU0280rXDUrSvgbZZy22ZsaVaNmjeHHr08L6AN96ew//+Opb9Fs7hmA8/Zp/Jk70JJACdO1PStSslXbsytUM77v4yj8UbHHlmtaoMot0iLtZeWqQt43y3ZQt88sn2QD1zJsydC5s3e/e3aeP1ri+/3AvYxcVJmVAVTqLb78Urpa+BZCwF8DQonV3ObVO/oaL9MdD+GAB237yBP+1dSbfVi71ANmkSvPACJwDvNGrEFy3asqBVez5r1Y7PW+7Ji5/NJ7/vKZx5/IERe2vx9CD7d+8UMreacIWGc976MzWDdVmZV5sNsPPOXo/697/3gnXXrlCU3t5luj6NJO01kKyiAJ4GoXp1Kxo35ZZ1Bbw/8CLvhupgN2sWf3viZYqWfsaBKxdz+sL/0qi6gGw4sOuuvNZ0Nz5tvjtLWrShfOfd+Kb5rnzTbFfy9ixi6KRPYu5B1uzZx5RbdQ6+/dYbXKz7tWSJV365YoV37A47eKmPvn23B+v9969VJRIE6eoJx/0aSE7RYlZpEG72pUHIWYA1j9+x8ifar/2aDmu8r9s75bNy9kdULvyUNt+v2h7ct9rUqDFrmu7M6oKdWVOwMz/u0ISNjXdkQ34Tep/QCXbayVsbvWlT7//5+bWfvKrKm3BolGcAAAgrSURBVLi0YUPorzVrvLr3777zBhU3bapzUebVyLdvD507bw/Whx7qrfCXoGQP4qnSQ4LA90FMiV+svbqax/+UvyOftu7Ap607UFRYwO0DTmI3vEDz6MR5VC0r52C3nis67sCRO2xk9IQy8td8x64bvqewYj1t1n9HQeVGmm3ZBCPKvCD800/RNdysdsAvKIAWLbw0xyGHePnqoiJo29b7t6jIW5a37h8Fn6RigFE9YQkyBfA0iDW/Gc3x4aoRmp8YRQ9y82avl/3jj9sHD6uZbQ/YO+wQqJrqVA0wqtJDgkoBPEZ+fGQv6VJE2ZLVjJy+lC3Oqy7p9bPwQSKRXmBUj23cmNJF6zKul5n2ckeRNFMAj0G8H9lD7Vc5blY5W7aOP2xxjnGzyilu37Leeeo+Np4p9A31IJOdikhWnjrWVJQmvUi2CdaQf8BF+sgeTnVwLF9bgcMLjiOmfRXVeUI99rbx8yidXe7XJQHxXVe0knkNoRYCC5eKStXPUiSVFMBjEMtH9tLZ5XQbMoWbRs+pFxyjXUUumYE10vM2dHssknkNdVfvKyosCFsdkqqfpUgqKYUSg2g/spfOLqf/mLlUVsVWoln3PKnK8Saz1jnZ1xDtAKPy5ZKN1AOPQbQf2e+a8FGDwbtuLUeo80QqK/RTLKmIWKXqGjKlHSJ+UgCPQbQf2avXbw6nID+Pi49u1+B5khlYa4olFRFKdbqo44CJdBsypVZeOVXX0JCgtEPET5qJmQQdBkwMe19RjNUPQa+ciHbd6iBcQ1DaIRKrpG9qHI1cCeBd7nmr3jKw4O2oMvvOX6ahRckTyLXDk0DBX9IpqZsaS22DzjqI/LzaWe78PGPQWQelqUXJkwuDgypBlKBSAE+Cki5FDD3vsFo55aHnHZaVPbZcGBxUCaIElcoIkyRX1s/IhXWrc+FThmQm9cAlIYlWsGSCXPiUIZlJPXBJWKRPG9kw+JcLnzIkMymAS9Kka0Ngv2lNcAkqBfAUyYaeaKzStSFwMuTKmIZkFgXwFMiWnmisNPgnklwaxEyBXC1D0+CfSHIpgKdArvZEtf6ISHIphZICyVyuNV2iyelr8E8kuRTAUyDbytBiyelr8E8keZRCSYFsm+ySqzl9kaBRDzxFsqknmqs5fZGgSagHbmanmdlCM1tkZgP8apQEm6pLRIIh7gBuZnnAX4DTgQOBC83sQL8aJsGl6hKRYEgkhdIVWOScWwxgZqOAc4CP/WiYBJeqS0SCIZEAXgQsrfH9MuCougeZ2TXANQDt2rVL4OkkSLIppy+SqRLJgdfdWB2g3v5szrlhzrli51xx69atE3g6ERGpKZEAvgzYq8b3ewLLE2uOiIhEK5EAPhPYz8w6mtkOQB9ggj/NEhGRhsSdA3fObTaz64E3gTxguHPuI99aJiIiESU0kcc59zrwuk9tERGRGGgqvYhIhtJU+gySi7v6iEh4CuAZIld39RGR8JRCyRBaAVBE6lIAzxBaAVBE6lIAzxBaAVBE6lIAzxBaAVBE6tIgZobQCoAiUpcCeAbRCoAiUpNSKCIiGUoBXEQkQymAi4hkKAVwEZEMpQAuIpKhzLl6u6Al78nMVgFLQtzVCvg2ZQ1JPl1P8GXbNel6gi+Ra2rvnKu3J2VKA3g4ZlbmnCtOdzv8ousJvmy7Jl1P8CXjmpRCERHJUArgIiIZKigBfFi6G+AzXU/wZds16XqCz/drCkQOXEREYheUHriIiMRIAVxEJEMFIoCb2b1m9qGZzTGzt8ysbbrblCgzG2pmn2y9rpfNrDDdbUqEmZ1vZh+ZWZWZZWx5l5mdZmYLzWyRmQ1Id3sSZWbDzWylmc1Pd1v8YGZ7mdm/zGzB1t+3G9PdpkSYWRMzm2Fmc7dez92+nj8IOXAz29k5t27r/28ADnTOXZvmZiXEzH4JTHHObTazBwGcc7emuVlxM7MDgCrgGeD3zrmyNDcpZmaWB3wKnAosA2YCFzrnPk5rwxJgZscDPwAvOOcOTnd7EmVmbYA2zrkPzKw5MAsoydTXyMwM2Mk594OZ5QP/AW50zk3z4/yB6IFXB++tdgLS/1clQc65t5xzm7d+Ow3YM53tSZRzboFzLtN3UO4KLHLOLXbObQJGAeekuU0Jcc69B6xOdzv84pz72jn3wdb/rwcWABm7CL7z/LD12/ytX77Ft0AEcAAzu9/MlgIXA3emuz0++xXwRrobIRQBS2t8v4wMDg7Zzsw6AF2A6eltSWLMLM/M5gArgcnOOd+uJ2UB3MzeNrP5Ib7OAXDO/cE5txcwArg+Ve1KREPXtPWYPwCb8a4r0KK5ngxnIW7L+E972cjMmgHjgJvqfELPOM65Lc65w/E+hXc1M99SXSnbUs05d0qUh/4TmAgMSmJzfNHQNZlZX6AHcLILwmBDA2J4jTLVMmCvGt/vCSxPU1skjK254nHACOfc+HS3xy/OubVm9i5wGuDLoHMgUihmtl+Nb88GPklXW/xiZqcBtwJnO+c2pLs9AniDlvuZWUcz2wHoA0xIc5ukhq2Dfn8FFjjn/pTu9iTKzFpXV6CZWQFwCj7Gt6BUoYwDOuFVOSwBrnXOlae3VYkxs0XAjsB3W2+alsmVNWZ2LvA40BpYC8xxznVPb6tiZ2ZnAI8CecBw59z9aW5SQsxsJPALvKVKVwCDnHN/TWujEmBmxwH/BubhxQOA251zr6evVfEzs0OBv+P9vjUCXnLO3ePb+YMQwEVEJHaBSKGIiEjsFMBFRDKUAriISIZSABcRyVAK4CIiGUoBXEQkQymAi4hkqP8HJUwgCzab/woAAAAASUVORK5CYII=\n"
     },
     "metadata": {
      "needs_background": "light"
     }
    }
   ],
   "source": [
    "plt.scatter(x, y)\n",
    "plt.plot(np.sort(x), y_predict2[np.argsort(x)], color='r')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "array([1.00237447, 0.47177799])"
     },
     "metadata": {},
     "execution_count": 17
    }
   ],
   "source": [
    "lin_reg2.coef_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "output_type": "execute_result",
     "data": {
      "text/plain": "2.0094722518223476"
     },
     "metadata": {},
     "execution_count": 18
    }
   ],
   "source": [
    "lin_reg2.intercept_"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ]
}